It is theorized that an island of nuclear stability exists in the 114-116 region of atomic mass. (Note by Sara: I think you mean atomic number.) I assume that even though we can't find such elements in our neighborhood, they may be produced in the supernova of a sufficiently large star.

My questions are as follows:

1. Does a theoretical formulation exist which can predict the isotope yields of elements for the supernova of a given stellar mass?

The elements with atomic numbers greater than that of iron are made in a variety of processes, notably s-process (s for slow) and r-process (r for rapid) neutron capture. The way it works is this: you start out with a seed atom, say (56,26)Fe. You're in a region of high neutron flux (e.g. a supernova), so neutrons start to pile up on your atom. After you collect 6 neutrons, your atom becomes (62,26)Fe, which is unstable to beta decay on a time scale (about 1 minute, in this case) shorter than the time between neutron captures. Before it can collect any more neutrons, it beta decays to (62,27)Co, which beta decays to (62,28)Ni, which is stable. Now neutrons start to collect on the Ni, and so it goes, stepping through the periodic table. When the atomic number or mass number gets too high, however, neutron capture induces fission. Whether the island of stability can be reached therefore depends on the maximum atomic number that can support the r-process described above without induced fission occuring. Once the island of stability was predicted, people started writing lots of papers saying both yes, no and maybe to the question of whether the island of stability could be reached by the r-process. The field settled at a solid "maybe" before it petered out. So, in answer to your question, no--people have yet to determine whether the stable superheavy elements are formed at all. It's a matter of the nature of the universe, rather than one finding a star that's massive enough. (Of course, the scenario I described is not the only possibility--it is possible that a binary system of a neutron star and a black hole would be a good place to form super-heavies, but I still have 3 questions left to answer so I'd better not get into that! At any rate, no one has really made a granite case that it's possible anywhere {except for a man-made accelerator}, so it's "maybe"'s across the board.)

Edit by Yubo Su (Jan 28, 2019): Observations of the electromagnetic counterpart to the neutron star-neutron star merger GW170817 seems to be consistent with theoretical models of r-process nucleosynthesis. Just as a starting point, this paper seems to suggest that elemental abundances due to the r-process as calculated here can roughly explain heavy element abundances in the Milky Way. Stay tuned as we discover more such events!

2. If so, can a prediction be made of the likelihood of finding stable super-heavy elements (114-116) in the universe? Has that already been done?

The lifetimes have been painstakingly predicted, but as the answer to #1 pointed out it, has yet to be proven whether these guys are formed at all, much less at what rates. Without that, you can't tell.

Edit by Yubo Su (Jan 28, 2019): Such heavy nuclei have actually been synthesized in labs and officially recognized; their decay lifetimes are of order milliseconds though, so after even just a second you would expect very little to remain (it would take just a few seconds for a Sun's mass of the element to decay away!). For instance, Oganesson (z=118) was discovered as early as 2002 and christened officially in 2015.

3. Do we know what to look for? (can we predict the spectral properties of these postulated isotopes)

Actually, predicting the chemistry of the superheavy elements is a whole neat field of its own--it turns out that when the atomic number is as high as that, you need some pretty fancy quantum mechanics to get it right. And if you then observe the element, you can see whether your fancy quantum mechanics got it right, or if it might need to be revised. People have done their best to predict everything down to the shoe sizes of these elements.

4. If so, is anyone looking?

Absolutely--and search actually does takes place within the bounds of the solar system. The material that makes up the solar system has already been through the stellar life cycle, so if superheavy elements were produced in supernovae, they could be found in our neighborhood (so many "super"'s--scientists can really lack originality sometimes). Rather than trying to detect radiation from the superheavies (which is unlikely), people have checked meteorites for evidence of cosmic rays made of superheavy elements and searched in samples from Earth and its moon, with no conclusive results.

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